itpro, your first paragraph was correct. The same volume of gas will contain the same number of molecules as the same volume of another gas. Avogadro's number (6*10^23) is the number of molecules of any gas in 1 mole of that gas at STP (273K, 1atm).
Your second paragraph is also very close to correct. You may be slightly off on the terms you're using, but ultimately you're trying to state that different gases have different specific heats and thus act as per Q=cm⌂T. In other words, different gases need different amounts of energy to raise their temperature because of their different masses.
Your third paragraph is the least correct.
You're talking about tyres heating up 'quicker', but 'time' has never been a factor in these equations so far. Going back to Q=mc⌂T, lower mass and specific heat capacity would suggest that the temperature (and therefore pressure) would change by a larger amount, but not quicker.
Using Helium would therfore increase the temperature range of the tyres as they heat up (note that I use the term 'heat' and 'temperature' carefully, they are very different things). I wouldn't have thought this would be desirable, a narrow temperature range would make your pressures more 'stable' as they get heat into them.
I would say that the best air to use would be one with a high mass and a high specific heat capacity. This means your pressures are chaning less and are therefore more predictable.
Therefore, what you want to be testing at the track is the range of pressures you get with different gases, the aim being to find a gas that lets you have the desired pressures in the tyres for the longest amount of time.
I've not explained that very well... I'll have another go later...
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